Question
Download Solution PDFदोन संख्यांचा सर्वात कमी सामान्य बहुविध आणि सर्वोच्च सामान्य घटक अनुक्रमे 30 आणि 5 आहेत. जर त्यांची बेरीज 25 असेल तर या दोन संख्यांमध्ये फरक किती असेल?
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFसंकल्पना:
दोन किंवा अधिक संख्यांच्या सर्वात मोठ्या सामान्य घटकास सर्वोच्च सामान्य घटक म्हणतात.
सर्वात लहान धन संख्या जी दोन किंवा अधिक संख्यांचा गुणाकार आहे त्याला किमान सामान्य गुणक म्हणतात
वापरलेले सूत्र:
LCM x HCF = दोन संख्यांचे उत्पादन
गणना:
संख्या a आणि b असू द्या
LCM x HCF = axb
⇒ axb = 150 ---- (1)
पेक्षा दिले,
⇒ a + b = 25 ----(2)
दोन्ही बाजूंनी चौरस घेऊन,
⇒ (a + b) 2 = 25 2
⇒ a 2 + b 2 + 2ab = 625
⇒ a 2 + b 2 + 2(150) = 625
⇒ a 2 + b 2 = 625 - 300 = 325 ----(3)
(a - b) 2 = a 2 + b 2 - 2ab
⇒ (a - b) 2 = 325 - 2(150)
⇒ (a - b) 2 = 325 - 300 = 25
⇒ a - b = 5 ----(4)
समीकरण (2) आणि (4) जोडल्यास, आपल्याला मिळते,
⇒ a + b + a - b = 25 + 5
⇒ 2a = 30
⇒ a = 30/2 = 15
a = 15 च्या जागी, समीकरणात (4)
⇒ a - b = 5,
⇒ 15 - b = 5
⇒ b = 15 - 5 = 10
∴ या दोन संख्यांमधील आवश्यक फरक = 15 - 10 = 5
Last updated on Jun 12, 2025
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